Delay analysis of Go-Back-N ARQ for correlated error channels

We investigate the performance of the Go-Back-N ARQ (Automatic Repeat reQuest) protocol over a wireless channel. Data packets are sent from transmitter to receiver over the wireless transmission channel. When a packet is received, the receiver checks whether it has been received correctly or not, and sends a feedback message to notify the transmitter of the condition of that packet. When the transmitter is notified of a transmission error, the incorrectly received packet is sent again, as well as every following packet.
Our modeling assumptions are based on two convictions. On the one hand, a good view of the performance of an ARQ protocol not only requires an analysis of the throughput, but also of the buffer behavior. Therefore, we offer a complete queueing analysis of the transmitter buffer, in addition to a throughput analysis. Secondly, due to the highly variable nature of the error process in wireless networks, we have to take error correlation explicitly into account.
Hence, we model the channel by means of a general Markov chain with $M$ states and a fixed error probability in every state. The transmitter buffer is modeled as a discrete-time queue with infinite storage capacity and independent and identically distributed packet arrivals from slot to slot.
We find concise expressions for the probability generating functions of the unfinished work and the packet delay of the transmitter buffer. Furthermore, we show explicit expressions for the mean and the variance of both system characteristics and we derive some heavy-load approximations. Finally, we provide some numerical examples.

@incollection{1007959,
abstract = {We investigate the performance of the Go-Back-N ARQ (Automatic Repeat reQuest) protocol over a wireless channel. Data packets are sent from transmitter to receiver over the wireless transmission channel. When a packet is received, the receiver checks whether it has been received correctly or not, and sends a feedback message to notify the transmitter of the condition of that packet. When the transmitter is notified of a transmission error, the incorrectly received packet is sent again, as well as every following packet.
Our modeling assumptions are based on two convictions. On the one hand, a good view of the performance of an ARQ protocol not only requires an analysis of the throughput, but also of the buffer behavior. Therefore, we offer a complete queueing analysis of the transmitter buffer, in addition to a throughput analysis. Secondly, due to the highly variable nature of the error process in wireless networks, we have to take error correlation explicitly into account.
Hence, we model the channel by means of a general Markov chain with \$M\$ states and a fixed error probability in every state. The transmitter buffer is modeled as a discrete-time queue with infinite storage capacity and independent and identically distributed packet arrivals from slot to slot.
We find concise expressions for the probability generating functions of the unfinished work and the packet delay of the transmitter buffer. Furthermore, we show explicit expressions for the mean and the variance of both system characteristics and we derive some heavy-load approximations. Finally, we provide some numerical examples.},
author = {De Turck, Koen and Wittevrongel, Sabine},
booktitle = {Mobility management and quality-of-service for decision making},
editor = {Kouvatsos, Demetres},
isbn = {9788792329202},
keyword = {queueing theory,performance,evaluation,wireless telecommunication,generating functions,automatic repeat request.},
language = {eng},
pages = {245--267},
publisher = {River Publishers},
series = {River Publishers' Series in Information Science and Technology},
title = {Delay analysis of Go-Back-N ARQ for correlated error channels},
year = {2009},
}